Why does everyone do it?
mike3
What is it about Cantor's theories that makes everyone want to try and
"critique"
them, anyway? And why do they always seem to generate long
discussions?
Why was it that what appears to be the longest thread here (9018 msgs)
started
off with a Cantor Critique?
Joshua Cranmer
In case you didn't realize, many solved problems with simple problem
statements but complex underlying theories tend to be attacked by all
ranges of non-mathematically-inclined people. For example, Gödel's
Incompleteness theorems, Fermat's Last Theorem, etc.
The fact that some of Cantor's work is both surprising and yet simple to
explain means that people work extra hard to find flaws in a fundamental
basis of mathematics that has existed for over a century.
David C. Ullrich
<da6a24d2-084e-4fa5...@b30g2000prf.googlegroups.com>,
mike3 <mike...@yahoo.com> wrote:
> Hi.
>
> What is it about Cantor's theories that makes everyone want to try and
> "critique"
> them, anyway?
People can't imagine an infinite set so big that it can't even
be "listed". And they think that if they can't imagine it
then it can't exist.
> And why do they always seem to generate long
> discussions?
Because they're unable to understand simple arguments, eg
the proof that |P(S)| > |S|, and unable or unwilling to
follow simple explanations of the errors in their refutations.
> Why was it that what appears to be the longest thread here (9018 msgs)
> started
> off with a Cantor Critique?
--
David C. Ullrich
Virgil
Joshua Cranmer <Pidg...@gmail.com> wrote:
Before Cantor's theorem, some favorites of kooks were claims of having
constructed "the quadrature of the circle", "the duplication of the
cube", or "the trisection of an arbitrary angle".
Dave L. Renfro
> Before Cantor's theorem, some favorites of kooks
> were claims of having constructed "the quadrature
> of the circle", "the duplication of the cube", or
> "the trisection of an arbitrary angle".
I suspect the eroding of geometry in high school
and college math classes (except for math education
majors) over the past century has played a major
role in why you don't see this stuff discussed.
There are exceptions, of course (see [1] & [2]),
but I suspect these are almost always people fairly
old and/or educated outside of the U.S. or its close
allies.
[1] http://mathforum.org/kb/message.jspa?messageID=6095104
http://www.pythagorascode.org/
[2] http://tinyurl.com/68mzhj
Domingo Gomez Morin's sci.math posts on the dangers of
teaching children about hyperspace ideas.
Dave L. Renfro
Mensanator
Look at sci.physics. Crackpots gravitate to that which
YOU can't easily refute unless you have a cyclotron in your
basement.
Same with math. Since YOU can't make a completed infinity,
concepts involving infinities attract crackpots.
And it helps if the personna involved were Jewish.
Over on sci.peanuts, the crackpots all attack
George Washington Carver.
Gerry Myerson
<be78dffc-da37-414e...@s50g2000hsb.googlegroups.com>,
Mensanator <mensa...@aol.com> wrote:
Who was, to the best of my knowledge, not Jewish.
Neither was Cantor, and if the crackpots knew that,
maybe they'd leave him alone.
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
Bill Taylor
> Before Cantor's theorem, some favorites of kooks were claims of having
> constructed "the quadrature of the circle", "the duplication of the
> cube", or "the trisection of an arbitrary angle".
Yes, interestingly those types seem to have died out at last.
Odd, because there were still some angle-trisectors around in
the 50s and 60s.
No doubt in Hellenistic times there were masses of 2nd-rate
mathematicians spending their lives trying to convince
people that they had a proof of the commensurability
of the square root of two.
<sigh>
----------------------------------------
I'm a little crackpot short and stout.
Don't ask my handle, let me spout.
When I get all steamed up then I shout,
Snip a poster - flame the lout.
----------------------------------------
Larry Hammick
"mike3" <mike...@yahoo.com> wrote in message
news:da6a24d2-084e-4fa5...@b30g2000prf.googlegroups.com...
Today it's the cranks who go on and on about Cantor, but in Cantor's own
time, some of the biggest hitters in the game (including Poincaré and
Kronecker) found plenty to complain about over infinite ordinals and the
axiom of choice and so on. Formalizing these things took time, and of course
the cranks don't make the effort to determine that this business has been
satisfactorily worked out.
Nowadays computers play a fairly big role in the Theory of Crankery. It used
to be the ruler and compass, but the computer has taken over their role. If
no amount of RAM will hold an infinite ordinal, then there are no infinite
ordinals, the thinking goes. There's no infinite axiom of choice either,
since even a 64-bit CPU can't flip all those bits.
And on top of those factors, there are the inexorable workings of Hammick's
Law of Thread Length: The length of a thread is inversely proportional to
its value. A law of nature. No getting around it.
LDH
P.S. Hammick's Laws in the theory of crankery should not be confused with
Hammick's Rule in organic chemistry.
http://en.wikipedia.org/wiki/Dalziel_Hammick
By some odd coincidence, Dalziel was my dad's name and is my middle name. :D
Mensanator
wrote:
> In article
> <be78dffc-da37-414e-b175-7b56c74e5...@s50g2000hsb.googlegroups.com>,
>
>
>
>
>
> Mensanator <mensana...@aol.com> wrote:
> > On Aug 5, 1:23 pm, mike3 <mike4...@yahoo.com> wrote:
> > > Hi.
>
> > > What is it about Cantor's theories that makes everyone want to try and
> > > "critique"
> > > them, anyway? And why do they always seem to generate long
> > > discussions?
> > > Why was it that what appears to be the longest thread here (9018 msgs)
> > > started
> > > off with a Cantor Critique?
>
> > Look at sci.physics. Crackpots gravitate to that which
> > YOU can't easily refute unless you have a cyclotron in your
> > basement.
>
> > Same with math. Since YOU can't make a completed infinity,
> > concepts involving infinities attract crackpots.
>
> > And it helps if the personna involved were Jewish.
>
> > Over on sci.peanuts, the crackpots all attack
> > George Washington Carver.
>
> Who was, to the best of my knowledge, not Jewish.
He certainly wasn't a WASP.
> Neither was Cantor,
Possibly. He didn't practice Judaism. It's not known one
way or the other whether he had Jewish ancestors.
> and if the crackpots knew that,
> maybe they'd leave him alone.
Don't know many NAZIs, eh?
mike3
> On Aug 5, 1:23 pm, mike3 <mike4...@yahoo.com> wrote:
>
> > Hi.
>
> > What is it about Cantor's theories that makes everyone want to try and
> > "critique"
> > them, anyway? And why do they always seem to generate long
> > discussions?
> > Why was it that what appears to be the longest thread here (9018 msgs)
> > started
> > off with a Cantor Critique?
>
> Look at sci.physics. Crackpots gravitate to that which
> YOU can't easily refute unless you have a cyclotron in your
> basement.
>
And so they can "get away" (or think they can) with it since
99.99% of the people on the group either do not have access
to a cyclotron, or if they did whoever owns it probably would
not let htem use it for that purpose, so...
> Same with math. Since YOU can't make a completed infinity,
> concepts involving infinities attract crackpots.
>
What does that mean, even, a "completed" infinity?
> And it helps if the personna involved were Jewish.
>
How does that help it? Is it some sort of racism/religionism/
other type of discriminatory belief?
mike3
Ah, and I'll bet it is ALSO why they go after Relativity so much
on sci.physics -- because Einstein was JEWISH!!!!!!!!!!!
Mensanator
Try doing a Google search on "tom potter".
>
>
>
> > > Over on sci.peanuts, the crackpots all attack
> > > George Washington Carver.- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
Gerry Myerson
<ce0d2bfb-8f30-49fc...@v26g2000prm.googlegroups.com>,
mike3 <mike...@yahoo.com> wrote:
I don't know about sci.physics - I never go there - but it is certainly
true that at least some of the crankish opposition to relativity is tied
in with anti-Jewish diseases.
Meanwhile, you asked about completed infinity. Back in the old days,
no one would have spoken of "the set of all integers." It was OK to say
that there were more integers than any pre-assigned number, but since
you could never complete the process of rounding them all up to put
into one set, you couldn't speak of the completed infinity of integers.
So questions about one infinite set being bigger than another didn't
arise, as people didn't accept the existence of infiniite sets in the
first place.
Mensanator
> On Aug 5, 4:06�pm, Mensanator <mensana...@aol.com> wrote:
>
>
>
>
>
> > On Aug 5, 1:23�pm, mike3 <mike4...@yahoo.com> wrote:
>
> > > Hi.
>
> > > What is it about Cantor's theories that makes everyone want to try and
> > > "critique"
> > > them, anyway? And why do they always seem to generate long
> > > discussions?
> > > Why was it that what appears to be the longest thread here (9018 msgs)
> > > started
> > > off with a Cantor Critique?
>
> > Look at sci.physics. Crackpots gravitate to that which
> > YOU can't easily refute unless you have a cyclotron in your
> > basement.
>
> And so they can "get away" (or think they can) with it since
> 99.99% of the people on the group either do not have access
> to a cyclotron, or if they did whoever owns it probably would
> not let htem use it for that purpose, so...
>
> > Same with math. Since YOU can't make a completed infinity,
> > concepts involving infinities attract crackpots.
>
> What does that mean, even, a "completed" infinity?
Don't ask me. I'm neither a crackpot nor a
mathematician.
>
> > And it helps if the personna involved were Jewish.
>
> How does that help it? Is it some sort of racism/religionism/
> other type of discriminatory belief?
Not necessarily a belief. Many of these endless
threads are as much due to trolls as to crackpots.
You should learn the difference. A troll doesn't
necessarily believe what he writes, he's just
trying to cause trouble. Crackpot math, pseudo-
science, racism/religionism/, it's all the same
to a troll. Anything to get people looking in his
direction.
lwa...@lausd.net
I believe it's because infinitary set theory is a bit
counterintuitive, as opposed to finite math. A post
declaring "1 = 2" or another formula whose negation
is a theorem of ZF-Infinity would hardly last 9000
posts, but a post declaring set theory including the
Axiom of Infinity to be inconsistent will result in
those super-long threads.
Mariano Suárez-Alvarez
The display of trust in the US education system implicit
in this comment is quite rare and optimistic ;-)
-- m
Han de Bruijn
> And on top of those factors, there are the inexorable workings of Hammick's
> Law of Thread Length: The length of a thread is inversely proportional to
> its value. A law of nature. No getting around it.
Hey ! Thought *I* had CopyRighted _that_ one ! :-)
Han de Bruijn
amy666
> In article
> <ce0d2bfb-8f30-49fc...@v26g2000prm.goog
wasnt it something like this :
einstein said :
if relativity will be a succes , germans will call me german.
swiss will call me a citizen of switserland.
and french will call me a scientist.
if relativity fails
french will call me swiss
swiss will call me german
and germans will call me a jew.
>
> Meanwhile, you asked about completed infinity. Back
> in the old days,
> no one would have spoken of "the set of all
> integers." It was OK to say
> that there were more integers than any pre-assigned
> number, but since
> you could never complete the process of rounding them
> all up to put
> into one set, you couldn't speak of the completed
> infinity of integers.
> So questions about one infinite set being bigger than
> another didn't
> arise, as people didn't accept the existence of
> infiniite sets in the
> first place.
>
> --
> Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for
> email)
regards
tommy1729
Dave L. Renfro
>> There are exceptions, of course (see [1] & [2]),
>> but I suspect these are almost always people fairly
>> old and/or educated outside of the U.S. or its close
>> allies.
Mariano Suárez-Alvarez wrote:
> The display of trust in the US education system implicit
> in this comment is quite rare and optimistic ;-)
My point (in case someone didn't get it) was that so little
math is taught today in the US pre-college education system
(or so it seems -- see [1], [2], & [3]) that its graduates
are rarely even exposed to the subject matter necessary
to be a crank in these other things (squaring the circle,
trisecting an angle, etc.).
[1] http://www.stolaf.edu/other/extend/Expectations/byrd.html
(Senator) Robert Byrd's 1997 speech on the Senate floor
[2] http://www.claytonmathmatters.com/krantz.pdf
Steven G. Krantz's essay on the textbook series
"Contemporary Math in Context"
[3] http://mathforum.org/kb/message.jspa?messageID=6153067
http://mathforum.org/kb/message.jspa?messageID=6179108
My comments on the core-plus math textbook series
Dave L. Renfro
MoeBlee
> On Aug 5, 6:57 pm, Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email>
> wrote:
> > Who was, to the best of my knowledge, not Jewish.
> > Neither was Cantor,
>
> Possibly. He didn't practice Judaism. It's not known one
> way or the other whether he had Jewish ancestors.
He was a devout Protestant.
MoeBlee
Larry Hammick
"Han de Bruijn"
to find that someone else had already been there, a mere decade or two
earlier ;)
LH
mike3
Hmm. And Cantor theory just happens to be a favorite
thing to use, then.
mike3
Hmm. And I'd suppose the higher the person's level of
resistance to "counterintuitive" ideas the longer he'd
try to keep the thread going...
Neil W Rickert
>On Aug 6, 7:49 am, Virgil <Vir...@gmale.com> wrote:
>> Before Cantor's theorem, some favorites of kooks were claims of having
>> constructed "the quadrature of the circle", "the duplication of the
>> cube", or "the trisection of an arbitrary angle".
>Yes, interestingly those types seem to have died out at last.
>Odd, because there were still some angle-trisectors around in
>the 50s and 60s.
Blame it all on the "new math". They don't teach Euclidean geometry
anymore. Hence no circe squarers and no angle trisectors. They now
teach set theory, leading to wannabe Cantor debunkers.
ju...@diegidio.name
Because that is where lie the foundations of contemporary mathematics,
and on the correctness of those foundations relies the correctness of
the whole building.
Also note that such correctness is not only the correctness of our
calculations: even more importantly, it is the "official" correctness
of our logic, i.e. our rational reasoning, with a very significant (as
much as silenced) impact on what is relevant and the shape of the
arguments allowed *in the court* (there is a discipline called:
metajuridics).
And then maybe you can glimpse what is really at stake "with Cantor".
-LV
MoeBlee
> Also note that such correctness is not only the correctness of our
> calculations: even more importantly, it is the "official" correctness
> of our logic, i.e. our rational reasoning, with a very significant (as
> much as silenced) impact on what is relevant and the shape of the
> arguments allowed *in the court* (there is a discipline called:
> metajuridics).
>
> And then maybe you can glimpse what is really at stake "with Cantor".
Yeah, O.J. got away with murder because of Cantor. The U.S. Supreme
Court ruled for Bush in 2000 because of Zermelo-Fraenkel set theory.
MoeBlee
Mariano Suárez-Alvarez
> On 5 Aug, 19:23, mike3 <mike4...@yahoo.com> wrote:
>
> > Hi.
>
> > What is it about Cantor's theories that makes everyone want to try and
> > "critique"
> > them, anyway? And why do they always seem to generate long
> > discussions?
> > Why was it that what appears to be the longest thread here (9018 msgs)
> > started
> > off with a Cantor Critique?
>
> Because that is where lie the foundations of contemporary mathematics,
> and on the correctness of those foundations relies the correctness of
> the whole building.
Actualy, I think that it is a subject that appears
much more accessible and should-be-common-sense (I was
taught the elements of set theory in kindergarden, and
I was shocked when I was given the technical definition
of cardinal numbers to find that it was essentially
the same notion I had been introduced to when I was 4
or 5)
It is quite unlikely that someone is going to
start a thread providing a critique of the proof
of the John-Nirenberg inequality, of the Cunz-Quillen
theorem stating that cyclic homology satisfies
excision, of the approach taken by Berthelot in
constructing crystalline cohomology or on the soundness
of Drinfel'd approach to the study of the absolute Galois
group through the theory of quantum groups. Doing so
would require years and years of study in
order to even construct a mental picture of what it
is that one is attempting to do in those contexts.
-- m
ju...@diegidio.name
<mariano.suarezalva...@gmail.com> wrote:
> On Aug 6, 5:14 pm, ju...@diegidio.name wrote:
> > On 5 Aug, 19:23, mike3 <mike4...@yahoo.com> wrote:
>
> > > Hi.
>
> > > What is it about Cantor's theories that makes everyone want to try and
> > > "critique"
> > > them, anyway? And why do they always seem to generate long
> > > discussions?
> > > Why was it that what appears to be the longest thread here (9018 msgs)
> > > started
> > > off with a Cantor Critique?
>
> > Because that is where lie the foundations of contemporary mathematics,
> > and on the correctness of those foundations relies the correctness of
> > the whole building.
>
> Actualy, I think that it is a subject that appears
> much more accessible and should-be-common-sense
Pardon me, but this is BS. What is at stake _is_ very significant,
despite that some might find the argument trivial. And it even isn't.
Your problem, around here, is that you have lost the sensibility -- or
the energy -- to appreciate the difference(s).
-LV
mike3
> On 6 Aug, 21:26, Mariano Suárez-Alvarez
>
>
>
> <mariano.suarezalva...@gmail.com> wrote:
> > On Aug 6, 5:14 pm, ju...@diegidio.name wrote:
> > > On 5 Aug, 19:23, mike3 <mike4...@yahoo.com> wrote:
>
> > > > Hi.
>
> > > > What is it about Cantor's theories that makes everyone want to try and
> > > > "critique"
> > > > them, anyway? And why do they always seem to generate long
> > > > discussions?
> > > > Why was it that what appears to be the longest thread here (9018 msgs)
> > > > started
> > > > off with a Cantor Critique?
>
> > > Because that is where lie the foundations of contemporary mathematics,
> > > and on the correctness of those foundations relies the correctness of
> > > the whole building.
>
> > Actualy, I think that it is a subject that appears
> > much more accessible and should-be-common-sense
>
> Pardon me, but this is BS. What is at stake _is_ very significant,
> despite that some might find the argument trivial. And it even isn't.
> Your problem, around here, is that you have lost the sensibility -- or
> the energy -- to appreciate the difference(s).
>
So are you saying then that it is stupid to feel it "appears"
accessible? I though the "debates" in these threads was about
whether or not it was "TRUE". Whole different topic.
I'm confused, could you please help alleviate it?
Mensanator
No Axiom of Choice, eh?
>
> MoeBlee
ju...@diegidio.name
It is stupid to be talking about what is irrelevant, only.
> I though the "debates" in these threads was about
> whether or not it was "TRUE". Whole different topic.
Indeed, that's it.
> I'm confused, could you please help alleviate it?
Logic is power when man is irrational. As Socrates used to say:
alleviate yourself...
-LV
amy666
not to mention global warming , internet trojans, roswell and 9/11 :p
no really, your sounding cranky MoeBlee :p
MoeBlee
> not to mention global warming , internet trojans, roswell and 9/11
I didn't know about that. But of course I believe you.
MoeBlee
ju...@diegidio.name
Italy has been recently quite known for that thing of the ad personam
laws: not only Berlusconi and friends got out of all personal troubles
with it, the whole country -- the little that there was -- has been
plundered and is as bankrupt as it can be.
Exact same thing is happening at the global level, with Corporations
and the WTO: they make the global laws, they make their own laws. But
Corps have nobody to sell to, so it's even more evil, just about the
self-sustainment of this regime of power by ignorance.
They have started by hacking the very notion of "democracy". But this
one happened with the French revolution, so a long story if one is
only interested in calculations.
-LV
> MoeBlee
David C. Ullrich
>On 6 Aug, 21:26, Mariano Suárez-Alvarez
><mariano.suarezalva...@gmail.com> wrote:
>> On Aug 6, 5:14 pm, ju...@diegidio.name wrote:
>> > On 5 Aug, 19:23, mike3 <mike4...@yahoo.com> wrote:
>>
>> > > Hi.
>>
>> > > What is it about Cantor's theories that makes everyone want to try and
>> > > "critique"
>> > > them, anyway? And why do they always seem to generate long
>> > > discussions?
>> > > Why was it that what appears to be the longest thread here (9018 msgs)
>> > > started
>> > > off with a Cantor Critique?
>>
>> > Because that is where lie the foundations of contemporary mathematics,
>> > and on the correctness of those foundations relies the correctness of
>> > the whole building.
>>
>> Actualy, I think that it is a subject that appears
>> much more accessible and should-be-common-sense
>
>
>Pardon me, but this is BS. What is at stake _is_ very significant,
Of course the question of whether Cantor's proof of the
uncountability of the reals is correct is a very important
question.
But it's also a trivial question. Yes, the proof is correct.
>despite that some might find the argument trivial. And it even isn't.
Not sure which "argument" you're referring to. The argument showing
that |P(A)| > |A| is in fact trivial. We see a lot of explanations why
it's wrong here on sci.math. Those explanations are always either
wrong or not-even-wrong ("not-even-wrong" meaing that the
supposed argument is so incoherently presented that one cannot
pinpoint the error because it's not clear what the statements in
the argument even _mean_.)
>Your problem, around here, is that you have lost the sensibility -- or
>the energy -- to appreciate the difference(s).
>
>-LV
>
>
>> (I was
>> taught the elements of set theory in kindergarden, and
>> I was shocked when I was given the technical definition
>> of cardinal numbers to find that it was essentially
>> the same notion I had been introduced to when I was 4
>> or 5)
>>
>> It is quite unlikely that someone is going to
>> start a thread providing a critique of the proof
>> of the John-Nirenberg inequality, of the Cunz-Quillen
>> theorem stating that cyclic homology satisfies
>> excision, of the approach taken by Berthelot in
>> constructing crystalline cohomology or on the soundness
>> of Drinfel'd approach to the study of the absolute Galois
>> group through the theory of quantum groups. Doing so
>> would require years and years of study in
>> order to even construct a mental picture of what it
>> is that one is attempting to do in those contexts.
>>
>> -- m
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
Han de Bruijn
> Of course the question of whether Cantor's proof of the
> uncountability of the reals is correct is a very important
> question.
>
> But it's also a trivial question. Yes, the proof is correct.
Preaching like the pope, saying "Of course the question of whether G*d
exists is a very important question. But it's also a trivial question.
Yes, G*d exists."
Han de Bruijn
Tonico
*********************************************************
No, no, no, no, no, Han: don't crank around again. It's no preaching,
it's a PROVABLE fact that any medium-level undergraduate student can
easily prove.
Now, some non-mathematicians don't want to accept or just are unable
to understand that and thus they think it is like preaching: it is
not, it is mathematics, in fact pretty basic one.
Regards
Tonio
Han de Bruijn
> On Aug 7, 2:20 pm, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL> wrote:
>
>>David C. Ullrich wrote:
>>
>>>Of course the question of whether Cantor's proof of the
>>>uncountability of the reals is correct is a very important
>>>question.
>>
>>>But it's also a trivial question. Yes, the proof is correct.
>>
>>Preaching like the pope, saying "Of course the question of whether G*d
>>exists is a very important question. But it's also a trivial question.
>>Yes, G*d exists."
>
> *********************************************************
>
> No, no, no, no, no, Han: don't crank around again. It's no preaching,
> it's a PROVABLE fact that any medium-level undergraduate student can
> easily prove.
>
> Now, some non-mathematicians don't want to accept or just are unable
> to understand that and thus they think it is like preaching: it is
> not, it is mathematics, in fact pretty basic one.
>
> Regards
> Tonio
Sure, Tonio, if you accept all the premises that lead to the conclusion.
That's not much different of what the pope does. And that's exactly the
essence of my and other's "cranking around".
Han de Bruijn
Tonico
*************************************************************
Of course if one accept the premises...what is called maths. Now, you
may be trying to say that there can be OTHER premises that can lead to
other conclusion, just like the different geometries we get from
assuming different things with respect to Euclid's 5th postulate.
But hey: let's see that other premises and then we shall judge, uh?
So far, most people cranking/trolling or just merely being curious
about this stuff just try to "prove" set theory or Cantor's Proof or
Cantor's Diagonalization Method or something else "wrong", and they
usually do so saying "it is illogical", "it is nonsensical", "it is
absurd", etc., a la WM.
What about giving some set ...*gulp*...ok, let's say some "bunch" of
axioms over which we'll get some result you like it more? Oh, but
there's a problem: that'd require way more knowledge than usually
found in cranks, so...let's just keep on attacking without any reason.
Just saying it doesn't make sense just because it does not make sense
to you is hardly serious stuff, Han.
Once again: for any set X, |X| < |P(X)|, and this is a rather easy,
short proof (not dogma, not divide recet, but just using pretty
elementary rules of logic and maths).
Wanna try something different using New York State's boxing rules?
Fine, give it a shot...and then we shall see.
Regards
Tonio
MoeBlee
It's a trivial fact about FINITE sequences, that there is a finite
sequence of formulas that uses only rules of INTUITIONISTIC logic
(from just one instance of the axiom schema of separation) that no set
maps onto its power set.
MoeBlee
MoeBlee
> Sure, Tonio, if you accept all the premises that lead to the conclusion.
No, we don't have to accept the premises or the logic to see merely
that there is indeed a proof from those premises using only said
logic.
Don't confuse two separate questions:
(1) Is there a proof (a certain kind of finite sequence of formulas)
from the premises and with the logic?
(2) Do we agree with the conclusion of the proof?
Moreover, in this case, the only premise required is:
One instance of the principle that given property formalized in the
language, and given a set x, there is a subset y whose members are all
and only the members of x that have said property.
And the only logic needed is intutitionistic logic.
> That's not much different of what the pope does. And that's exactly the
> essence of my and other's "cranking around".
No, popes don't use formal axioms and formal rules of inference to
prove their various statements.
MoeBlee
Mike Kelly
> Tonico wrote:
>
> > On Aug 7, 2:20 pm, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL> wrote:
> >
> >>David C. Ullrich wrote:
> >>
> >>>Of course the question of whether Cantor's proof of the
> >>>uncountability of the reals is correct is a very important
> >>>question.
> >>
> >>>But it's also a trivial question. Yes, the proof is correct.
> >>
> >>Preaching like the pope, saying "Of course the question of whether G*d
> >>exists is a very important question. But it's also a trivial question.
> >>Yes, G*d exists."
> >
> > *********************************************************
> >
> > No, no, no, no, no, Han: don't crank around again. It's no preaching,
> > it's a PROVABLE fact that any medium-level undergraduate student can
> > easily prove.
> >
> > Now, some non-mathematicians don't want to accept or just are unable
> > to understand that and thus they think it is like preaching: it is
> > not, it is mathematics, in fact pretty basic one.
>
When we say "The proof is correct" we mean precisely that the premises
lead to the conclusion. There is no "accepting" involved.
> That's not much different of what the pope does. And that's exactly the
> essence of my and other's "cranking around".
No, you are a crank because you _still_ after _decades_ will not allow
yourself to learn what a proof is, or how axiomatic mathematics works.
ju...@diegidio.name
> On Wed, 6 Aug 2008 13:38:59 -0700 (PDT), ju...@diegidio.name wrote:
> >On 6 Aug, 21:26, Mariano Suárez-Alvarez
> ><mariano.suarezalva...@gmail.com> wrote:
> >> On Aug 6, 5:14 pm, ju...@diegidio.name wrote:
> >> > On 5 Aug, 19:23, mike3 <mike4...@yahoo.com> wrote:
>
> >> > > Hi.
>
> >> > > What is it about Cantor's theories that makes everyone want to try and
> >> > > "critique"
> >> > > them, anyway? And why do they always seem to generate long
> >> > > discussions?
> >> > > Why was it that what appears to be the longest thread here (9018 msgs)
> >> > > started
> >> > > off with a Cantor Critique?
>
> >> > Because that is where lie the foundations of contemporary mathematics,
> >> > and on the correctness of those foundations relies the correctness of
> >> > the whole building.
>
> >> Actualy, I think that it is a subject that appears
> >> much more accessible and should-be-common-sense
>
> >Pardon me, but this is BS. What is at stake _is_ very significant,
>
> Of course the question of whether Cantor's proof of the
> uncountability of the reals is correct is a very important
> question.
>
> But it's also a trivial question. Yes, the proof is correct.
Maybe it is not just a question of "correctness". Correctness is not
an absolute. Maybe is about "comprehension".
First, the matter -- as I get it -- boils down to the axioms one
happens to choose, and there is not only the ZF family. Nor deduction
from the axioms can make up any "evidence": axioms do need to be
"accepted".
Then, even "accepting" the Powerset Axiom, I still can't find anything
trivial in getting the result |P(N)|>|N|. Actually: I can't find
anything trivial in the very diagonal argument! Because the formal
procedures of proof are not always so clear-cut as one would naively
suppose, are they? The nearest is the furthest, and so I guess I am
just still learning.
BTW, I believe I am agreeing with Hans the Bruijn in the substance.
(To add my 2c to the polemic: each coin has two sides and, as a matter
of fact, counter-crankhood is no exception.)
-LV
MoeBlee
> On 7 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> First, the matter -- as I get it -- boils down to the axioms one
> happens to choose, and there is not only the ZF family. Nor deduction
> from the axioms can make up any "evidence": axioms do need to be
> "accepted".
That is not at issue. What is at issue is the simple fact that from
just ONE instance of the axiom schema of separation, and using just
intutionistic rules of inference, the result is provable. Whether you
accept intutionistic logic (a proper sublogic of classical logic) or
the axiom schema of separation is a DIFFERENT question. Meanwhile,
though, as to the MERE question of of whether there is indeed a proof
from said axiom with said rules is trivial - we see conspicuously, as
a matter of FINITE determination, that there is such a proof.
> Then, even "accepting" the Powerset Axiom,
We don't need the power set axiom to prove that there is no mapping
from any set x onto any set that has all subsets of x as members.
>I still can't find anything
> trivial in getting the result |P(N)|>|N|. Actually: I can't find
> anything trivial in the very diagonal argument! Because the formal
> procedures of proof are not always so clear-cut as one would naively
> suppose, are they?
The rules of inference used in the post can be made PRECISELY clear to
the extent that there is an algorithm that can check whether the rules
have been correctly applied or not. That is precise.
I keep saying these things over and over again, and just as you can
verify for yourself that these things are the case, but you just keep
ignoring while instead you continue to jabber on about what you
haven't actually taken the time to understand.
MoeBlee
MoeBlee
> each coin has two sides
I don't know what you think is the "other side" of the coin upon which
on one clearly visible side you can see, as a matter of FINITE
inspection, that there exists a certain finite sequence of formulas.
It seems that that "other side" is simply to close your eyes and
pretend that said finite sequence does not exist.
MoeBlee
ju...@diegidio.name
> On Aug 7, 12:09 pm, ju...@diegidio.name wrote:
>
> > On 7 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > First, the matter -- as I get it -- boils down to the axioms one
> > happens to choose, and there is not only the ZF family. Nor deduction
> > from the axioms can make up any "evidence": axioms do need to be
> > "accepted".
>
> That is not at issue.
And who are you to tell what is and what is not at issue?
Can you see the absurdity of your position?
I can appreciate your line of reasoning, moron. It's you who are blind
and now just a broken disk.
Although, on the other side: perfect job, including the accurate
snipping. You now are promoted aspiring troll.
The two side.
-LV
>
> MoeBlee
David C. Ullrich
<484f7529-1408-4fbd...@j22g2000hsf.googlegroups.com>,
ju...@diegidio.name wrote:
We all know that. It doesn't matter. There are people who
cannot understand that 2 + 2 = 4, and who will never understand
that no matter how hard they try. The existence of such people
doesn't mean there's anything non-trivial about adding 2 plus 2.
The present situation is worse, since as far as we can see you
haven't been trying to understand the correct proof, instead
you've been trying to make people believe your proof that it's
false (which "proof" is incoherent nonsense).
The definition of "trivial" is not "everyone, with no exceptions,
believes it". Nothing you've said about all this has any effect
whatever on the fact that the proof that |P(A)| > |A| is trivial.
--
David C. Ullrich
MoeBlee
> On 7 Aug, 20:20, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > On Aug 7, 12:09 pm, ju...@diegidio.name wrote:
>
> > > On 7 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > > First, the matter -- as I get it -- boils down to the axioms one
> > > happens to choose, and there is not only the ZF family. Nor deduction
> > > from the axioms can make up any "evidence": axioms do need to be
> > > "accepted".
>
> > That is not at issue.
>
> And who are you to tell what is and what is not at issue?
You can pursue any issue you want. But I can also say that certain of
your concerns are not at issue, in the sense that it is not even
DISAGREED that. e.g., you are not obligated to accept the axioms of
ZFC. I don't think there are very many people who would dispute that
if you reject the axioms and/or the system of logic then you would not
be expected to accept the theorems from those axioms and logic.
> I can appreciate your line of reasoning, moron. It's you who are blind
Interesting, since I AGREE with you that the conclusion of Cantor's
argument is not something you are intellectually obligated to accept
if you don't accept the axioms and rules of inference used to prove
the conclusion.
What I am trying to get you to recognize (it would help if you would
say that you do recognize it) is that the question of whether there
exists a proof from the axioms and rules is DIFFERENT from the
question of whether you accept those axioms and rules.
Moreover, you have not said exactly that you do reject the axiom
schema of separation and/or any rule of intutionistic logic used in
the proof.
And on another matter, you have not proven a contradiction of any
theorem of ZFC by using only the axioms and rules of inference of ZFC.
So, after the extensive help you were given on that matter, it would
help clarity if you would at least say now that you recognize that
you've not shown such a proof.
MoeBlee
David C. Ullrich
<bd8222b0-ebc7-44e8...@p25g2000hsf.googlegroups.com>,
ju...@diegidio.name wrote:
> On 7 Aug, 20:20, MoeBlee <jazzm...@hotmail.com> wrote:
> > On Aug 7, 12:09 pm, ju...@diegidio.name wrote:
> >
> > > On 7 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > > First, the matter -- as I get it -- boils down to the axioms one
> > > happens to choose, and there is not only the ZF family. Nor deduction
> > > from the axioms can make up any "evidence": axioms do need to be
> > > "accepted".
> >
> > That is not at issue.
>
>
> And who are you to tell what is and what is not at issue?
>
> Can you see the absurdity of your position?
>
> I can appreciate your line of reasoning, moron. It's you who are blind
> and now just a broken disk.
It's not just him. By your lights every mathematician on the
planet is blind, and you're the only one who can see the truth
here.
> Although, on the other side: perfect job, including the accurate
> snipping. You now are promoted aspiring troll.
>
> The two side.
>
> -LV
>
>
> >
> > MoeBlee
--
David C. Ullrich
David C. Ullrich
There's a big difference. The pope cannot prove that God exists.
I _can_ prove that |P(A)| > |A|. And the proof is very simple.
The fact that I don't write down that proof every time I mention
it does not imply that I'm appealing to authority.
> Han de Bruijn
--
David C. Ullrich
David C. Ullrich
Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
> Tonico wrote:
>
> > On Aug 7, 2:20 pm, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL> wrote:
> >
> >>David C. Ullrich wrote:
> >>
> >>>Of course the question of whether Cantor's proof of the
> >>>uncountability of the reals is correct is a very important
> >>>question.
> >>
> >>>But it's also a trivial question. Yes, the proof is correct.
> >>
> >>Preaching like the pope, saying "Of course the question of whether G*d
> >>exists is a very important question. But it's also a trivial question.
> >>Yes, G*d exists."
> >
> > *********************************************************
> >
> > No, no, no, no, no, Han: don't crank around again. It's no preaching,
> > it's a PROVABLE fact that any medium-level undergraduate student can
> > easily prove.
> >
> > Now, some non-mathematicians don't want to accept or just are unable
> > to understand that and thus they think it is like preaching: it is
> > not, it is mathematics, in fact pretty basic one.
> >
> > Regards
> > Tonio
>
> Sure, Tonio, if you accept all the premises that lead to the conclusion.
Just out of curiosity: Exactly which premise do you not accept?
> That's not much different of what the pope does. And that's exactly the
> essence of my and other's "cranking around".
>
> Han de Bruijn
--
David C. Ullrich
ju...@diegidio.name
> The present situation is worse, since as far as we can see you
> haven't been trying to understand the correct proof
You too: the correct proof of WHAT?
You guys *are* blind, but it's *you*, not the mathematicians.
Your "logic" is indeed a joke.
-LV
amy666
Democracy , what a funny word.
e.g. if that really existed , there would be no more taxes.
Because nobody wants to pay them.
the only place i know of , where there might be a little bit of democracy is probably switzerland , where you can ( or at least could have ) voted for LAWS instead of PEOPLE.
now that difference may seem small to you , but believe me its not.
and all these big countries like US , Canada , Russia , China , Japan , ... who talk about ' Democracy ' never talk about that !
" an inconvenient truth " id say.
but wait , isnt this the math forum ?
regards
tommy1729
" statisticly , i dont exist " tommy1729
Mensanator
The US isn't a democracy and has never pretended to be one.
It's a constitutional republic.
> Canada , Russia , China , Japan , ... who talk about ' Democracy ' never talk about that !
>
> " an inconvenient truth " id say.
>
> but wait , isnt this the math forum ?
>
> regards
>
> tommy1729
>
> " statisticly , i dont exist " tommy1729- Hide quoted text -
>
> - Show quoted text -
hagman
> On 7 Aug, 21:00, "David C. Ullrich" <dullr...@sprynet.com> wrote:
>
> > The present situation is worse, since as far as we can see you
> > haven't been trying to understand the correct proof
>
> You too: the correct proof of WHAT?
>
> You guys *are* blind, but it's *you*, not the mathematicians.
>
> Your "logic" is indeed a joke.
>
> -LV
>
Even though David mentions the theorem 2+2=4, I assume that the
term "the correct proof" refers to the ubiquitious theorem
|P(A)| > |A| instead.
Or do you have a problem with that other theorem?
hagman
MoeBlee
> On 7 Aug, 21:00, "David C. Ullrich" <dullr...@sprynet.com> wrote:
>
> > The present situation is worse, since as far as we can see you
> > haven't been trying to understand the correct proof
>
> You too: the correct proof of WHAT?
That there is no function from a set onto its power set.
Sheesh! We've been talking with you about it for hundreds of posts
over different threads.
MoeBlee
ju...@diegidio.name
Indeed.
"The proof of WHAT" means that you keep not addressing the issues that
are raised. You keep ignoring. You keep denying. You keep with your
broken disk.
Clearer now?
-LV
> MoeBlee
MoeBlee
I've addressed your remarks at virtually every turn in your ongoing
arguments. I have not ignored. And there is not a single correct
remark you have made that I have denied. You said a little while ago
that you wanted to learn about this subject. You've been given all
kinds of help, including from people much more knowledgable than I am.
But rather than LISTEN to that help, you've let your participation
dwindle now to just ineffective flailing about. I've given you the
mathematical explanations, at every juncture. If you won't come to
reason, at least ADDRESS those explanations, then I don't think
there's much more I can do for you.
MoeBlee
Tonico
> On Aug 7, 1:19 pm, ju...@diegidio.name wrote:
>
> > On 7 Aug, 21:00, "David C. Ullrich" <dullr...@sprynet.com> wrote:
>
> > > The present situation is worse, since as far as we can see you
> > > haven't been trying to understand the correct proof
>
> > You too: the correct proof of WHAT?
>
> That there is no function from a set onto its power set.
>
Moeblee probably meant to write "that there is no bijection between
any set and its power set".
Function between these two can be.
Regards
Tonio
David C. Ullrich
wrote:
I suspect he meant exactly what he wrote. Note the word "onto".
(If you didn't just miss that word maybe it's a language
problem or something: A function f from A _onto_ B
is a _surjective_ function: Every element of B is f(a)
for some a in A.)
>Regards
>Tonio
Han de Bruijn
Whether reasoning is formalized or not, as such, has nothing to do with
the correctness of a reasoning. Be convinced that the reasonings of the
Catholic Church are correct, _given_ their axioms. But you can disagree
with those axioms - as many people do. As mathematics keeps denying its
existence as a _science_, resemblance to a religion is quite a possible
alternative to consider.
Han de Bruijn
Han de Bruijn
> Han de Bruijn wrote:
>
>>Tonico wrote:
>>
>>>On Aug 7, 2:20 pm, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL> wrote:
>>>
>>>>David C. Ullrich wrote:
>>>>
>>>>>Of course the question of whether Cantor's proof of the
>>>>>uncountability of the reals is correct is a very important
>>>>>question.
>>>>
>>>>>But it's also a trivial question. Yes, the proof is correct.
>>>>
>>>>Preaching like the pope, saying "Of course the question of whether G*d
>>>>exists is a very important question. But it's also a trivial question.
>>>>Yes, G*d exists."
>>>
>>>*********************************************************
>>>
>>>No, no, no, no, no, Han: don't crank around again. It's no preaching,
>>>it's a PROVABLE fact that any medium-level undergraduate student can
>>>easily prove.
>>>
>>>Now, some non-mathematicians don't want to accept or just are unable
>>>to understand that and thus they think it is like preaching: it is
>>>not, it is mathematics, in fact pretty basic one.
>>
>>Sure, Tonio, if you accept all the premises that lead to the conclusion.
>
> When we say "The proof is correct" we mean precisely that the premises
> lead to the conclusion. There is no "accepting" involved.
The whole framework of formal _logic_ itself is built upon "accepting".
You _must_ start somewhere and at that very start invariably you should
ACCEPT things.
>>That's not much different of what the pope does. And that's exactly the
>>essence of my and other's "cranking around".
>
> No, you are a crank because you _still_ after _decades_ will not allow
> yourself to learn what a proof is, or how axiomatic mathematics works.
Keep dreaming about what I've learned or not.
I have a nice puzzle for you.
Given that 2^n is a natural, and 3^n is a natural (n is a number),
prove that n is a natural. Show us how axiomatic mathematics works.
Han de Bruijn
Han de Bruijn
> In article <7096$489ada71$82a1e228$29...@news1.tudelft.nl>,
> Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
>
>>David C. Ullrich wrote:
>>
>>>Of course the question of whether Cantor's proof of the
>>>uncountability of the reals is correct is a very important
>>>question.
>>>
>>>But it's also a trivial question. Yes, the proof is correct.
>>
>>Preaching like the pope, saying "Of course the question of whether G*d
>>exists is a very important question. But it's also a trivial question.
>>Yes, G*d exists."
>
> There's a big difference. The pope cannot prove that God exists.
The pope _can_ prove that God exists, _given_ his _own_ assumptions and
within his _own_ albeit informal overly correct logic.
> I _can_ prove that |P(A)| > |A|. And the proof is very simple.
Sure. But what has _this_ to do with the uncountability of the reals ?
> The fact that I don't write down that proof every time I mention
> it does not imply that I'm appealing to authority.
I believe you're serious.
Han de Bruijn
Han de Bruijn
> Just out of curiosity: Exactly which premise do you not accept?
Let's say that I still have trouble with the idea that infinity can be
completed, or finished. On the other hand, I'm working with it all day.
In very much the same way as going to church and not believing in God.
Han de Bruijn
Brian Chandler
Could you perhaps explain what you mean by "infinity" (whatever that
refers to, exactly) being "completed" or "finished". (I assume that
completed or finished refer to the same thing.)
I don't know of anything in the *subject matter* mathematics where
saying that something is "finished" makes sense. Of course a proof may
be finished or not, as may some elementary exericises. But a triangle
can't be "finished", nor can Klein's four-group. So what would it
mean for an infinite set (for example) to be "finished" (or "not
finished" for that matter)?
Brian Chandler
bits...@gmail.com
empty as well, then |P(A)| = 0 too. Or is P(A) containing an empty
subset, and hence have |P(A)| = 1 ?
- Carlos
Dave Seaman
If A is empty, then P(A) = {{}}, which is not empty. In fact, |P(A)| = 1.
--
Dave Seaman
Third Circuit ignores precedent in Mumia Abu-Jamal ruling.
<http://www.indybay.org/newsitems/2008/03/29/18489281.php>
riderofgiraffes
No, if A={} then P(A)={ {} }
Han de Bruijn
Oh ! How difficult that is ..
_The_ set of _all_ naturals does (actually) exist. Right?
Alternatively one could refuse to accept that _the_ set of naturals does
exist (as a complete infinity) and consider only initial segments of it.
As a matter of speech one could say then that _the_ set of naturals does
not exist. Or rather that it exists but it is unfinished. To be honest,
though, I'm not finished with this :-(
Han de Bruijn
Tonico
> On Thu, 7 Aug 2008 21:24:48 -0700 (PDT), Tonico <Tonic...@yahoo.com>
> wrote:
>
>
>
>
>
> >On Aug 8, 12:39 am, MoeBlee <jazzm...@hotmail.com> wrote:
> >> On Aug 7, 1:19 pm, ju...@diegidio.name wrote:
>
> >> > On 7 Aug, 21:00, "David C. Ullrich" <dullr...@sprynet.com> wrote:
>
> >> > > The present situation is worse, since as far as we can see you
> >> > > haven't been trying to understand the correct proof
>
> >> > You too: the correct proof of WHAT?
>
> >> That there is no function from a set onto its power set.
>
> >********************************************************
>
> >Moeblee probably meant to write "that there is no bijection between
> >any set and its power set".
> >Function between these two can be.
>
> I suspect he meant exactly what he wrote. Note the word "onto".
>
> (If you didn't just miss that word maybe it's a language
> problem or something: A function f from A _onto_ B
> is a _surjective_ function: Every element of B is f(a)
> for some a in A.)
>
Yes, I missed the word. My bad.
Tonio
Tonico
**********************************************************
Unless the catholic church accepted lately as formal dogma that "god
exists" (and thus no formal proof of existence required) , which I
highly doubt since one of its very , very weird dogmas is "god's
existence is provable by reason", then the answer is no: the church
hasn't yet proved any god's existence, and by "proved" I mean using
accepted logical inference rules.
Kant showed more than 200 years ago that the famous 5 proofs of god's
existence the church used to wave were utterly useless, and then he
(Kant) came up with his ridiculous moral argument (ridiculous because
it came from such a high intellect as Kant's).
Up to these days many christians, and among them catholics, still
clinge the old "last cause" argument, or even to the bizarre
ontological one.
So, as you can see, the pope can prove squat...at least as compred
with logical proofs. If you want to use arguments about "god's
existence is obvious when you smell a flower or when you see the smile
of a baby" then I can see nothing about that.
Regards
Tonio
Mike Kelly
No, the framework of formal logic has nothing to do with ACCEPTING.
Can you even define what it means to ACCEPT an axiom or ACCEPT a rule
of inference?
When we say "The proof is correct" we mean precisely that the premises
and the inference rules lead to the conclusion. What does whether or
not we ACCEPT the axioms (whatever that means) or ACCEPT the inference
rules (whatever that means) have to do with whether those axioms and
rules do, in fact, lead to the conclusion?
> >>That's not much different of what the pope does. And that's exactly the
> >>essence of my and other's "cranking around".
> >
> > No, you are a crank because you _still_ after _decades_ will not allow
> > yourself to learn what a proof is, or how axiomatic mathematics works.
>
> Keep dreaming about what I've learned or not.
Well, intelligence consists of reading between the lines, you know.
Mike Kelly
> David C. Ullrich wrote:
>
> > Just out of curiosity: Exactly which premise do you not accept?
>
> Let's say that I still have trouble with the idea that infinity can be
> completed, or finished.
I have trouble with that idea too, since I have no idea what you are
talking about, and seriously doubt you can coherently explain.
Mike Kelly
> David C. Ullrich wrote:
> > I _can_ prove that |P(A)| > |A|. And the proof is very simple.
>
> Sure. But what has _this_ to do with the uncountability of the reals ?
Do you _really_ not know? Are you just playing dumb?
There is a bijection between P(N) and R. So |R| = |P(N)|.
So |P(N)|>|N| implies |R| > |N|.
Mike Kelly
> Brian Chandler wrote:
>
> > Han de Bruijn wrote:
> >
> >>David C. Ullrich wrote:
> >>
> >>>Just out of curiosity: Exactly which premise do you not accept?
> >>
> >>Let's say that I still have trouble with the idea that infinity can be
> >>completed, or finished. On the other hand, I'm working with it all day.
> >>In very much the same way as going to church and not believing in God.
> >
> > Could you perhaps explain what you mean by "infinity" (whatever that
> > refers to, exactly) being "completed" or "finished". (I assume that
> > completed or finished refer to the same thing.)
> >
> > I don't know of anything in the *subject matter* mathematics where
> > saying that something is "finished" makes sense. Of course a proof may
> > be finished or not, as may some elementary exericises. But a triangle
> > can't be "finished", nor can Klein's four-group. So what would it
> > mean for an infinite set (for example) to be "finished" (or "not
> > finished" for that matter)?
>
> Oh ! How difficult that is ..
>
> _The_ set of _all_ naturals does (actually) exist. Right?
>
> Alternatively one could refuse to accept that _the_ set of naturals does
> exist (as a complete infinity) and consider only initial segments of it.
Your explanation of "complete infinity" uses the phrase "complete
infinity". Well done, I suppose.
Bonus points for "actually exist".
Tonico
***********************************************************
Oh, dear! This very same issue already triggered two long, long, very
looooong threads in this forum the last 2-3 years. In fact, the second
such threat still is on and well into its +9,000 posts.
And it is precisely the idea of "explain from a mathematical point of
view what do you mean by "infinity can be completed or finished" that
causes a huge flood of posts.
This seems to be a mistery worth the attention of great misteries'
researchers, like St. Agustin,Sherlock Holmes or Buffy the vampire
slayer.
Up to this day, not many people(if any at all) know what do Han and
others mean when they say that they have trouble with the idea of
infinity being completed...
Who knows, perhaps in the future...
Regards
Tonio
ju...@diegidio.name
On 7 Aug, 19:24, Mike Kelly <mikekell...@googlemail.com> wrote:
> Han de Bruijn wrote:
> > Tonico wrote:
> > > On Aug 7, 2:20 pm, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL> wrote:
>
> > >>David C. Ullrich wrote:
>
> > >>>Of course the question of whether Cantor's proof of the
> > >>>uncountability of the reals is correct is a very important
> > >>>question.
>
> > >>>But it's also a trivial question. Yes, the proof is correct.
>
> > >>Preaching like the pope, saying "Of course the question of whether G*d
> > >>exists is a very important question. But it's also a trivial question.
> > >>Yes, G*d exists."
>
> > > *********************************************************
>
> > > No, no, no, no, no, Han: don't crank around again. It's no preaching,
> > > it's a PROVABLE fact that any medium-level undergraduate student can
> > > easily prove.
>
> > > Now, some non-mathematicians don't want to accept or just are unable
> > > to understand that and thus they think it is like preaching: it is
> > > not, it is mathematics, in fact pretty basic one.
>
> > Sure, Tonio, if you accept all the premises that lead to the conclusion.
>
> When we say "The proof is correct" we mean precisely that the premises
> lead to the conclusion. There is no "accepting" involved.
Wrong. First: "logical validity" (or "correctness", as you put it), is
not "logical truth", so you still don't get the point. Second, and
more important: you are *even more wrong* because the rules for
logical validity are grounded into the rules for the ordinary
language, so that you are really clueless and your logic is just a
dogma.
> > That's not much different of what the pope does. And that's exactly the
> > essence of my and other's "cranking around".
>
> No, you are a crank because you _still_ after _decades_ will not allow
> yourself to learn what a proof is, or how axiomatic mathematics works.
No, it's you and friends who don't know what you are talking about,
and who make threads 9000+ posts long, by restating the same
trivialities and the same ad hominen insults over and over again, dumb
to anything else. Your logic is indeed just a dogma, the general dogma
of contemporary idiocy: deny acceptance, just give it for granted; the
perfect double-bind.
-LV
ju...@diegidio.name
Knowing more is good but not enough.
What are YOU going to DO with your knowledge?
Not waiting for an anwer... ;)
-LV
David C. Ullrich
Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
> David C. Ullrich wrote:
>
> > Just out of curiosity: Exactly which premise do you not accept?
>
> Let's say that I still have trouble with the idea that infinity can be
> completed, or finished.
How is "the idea the infinity can be completed, or finished",
a premise in the proof?
> On the other hand, I'm working with it all day.
> In very much the same way as going to church and not believing in God.
>
> Han de Bruijn
--
David C. Ullrich
David C. Ullrich
Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
If you said that the set of all natural numbers does not exist that
would be very curious, but at least it would be comprehensible.
Suggesting that "it exists but is unfinished" on the other hand
is completely opaque, until you explain what it means for a set
to be "finished".
If you mean "I don't believe there is any such thing as an infinite
set" it would be a better idea to say exactly that.
>To be honest,
> though, I'm not finished with this :-(
>
> Han de Bruijn
--
David C. Ullrich
MoeBlee
> No, it's you and friends who don't know what you are talking about,
> and who make threads 9000+ posts long, by restating the same
> trivialities
Basic mathematical results are stated over and over, because cranks
either SKIP recognizing them, misunderstand them, or mischaracterize
them each time.
> and the same ad hominen insults over and over again,
Actually, ad hominems are not always the same ones. And you, in
particular, can expect to get ad hominems for the fact that you are
clearly in bad faith in regards your earlier comments that you are
here to learn, that you encourage people to help you understand, while
you've since shown instead that you are not sincere in understanding
the actual mathematics of these matters. Other cranks get ad hominems
for other reasons, including their own forms of intellectual
dishonesty, rudeness, and smugness (while being completely incorrect
about the mathematics).
> dumb
> to anything else. Your logic is indeed just a dogma, the general dogma
> of contemporary idiocy: deny acceptance, just give it for granted; the
> perfect double-bind.
At least one hopes you don't think that is any kind of mathematical
argument.
MoeBlee
ju...@diegidio.name
> At least one hopes you don't think that is any kind of mathematical
> argument.
You just have a long way to go...
Just stop your insults please.
Or I'll start ignoring you.
Which would be a pity, as you are a cool guy.
-LV
>
> MoeBlee
Brian Chandler
> Brian Chandler wrote:
>
> > Han de Bruijn wrote:
> >
> >>David C. Ullrich wrote:
> >>
> >>>Just out of curiosity: Exactly which premise do you not accept?
> >>
> >>Let's say that I still have trouble with the idea that infinity can be
> >>completed, or finished. On the other hand, I'm working with it all day.
> >>In very much the same way as going to church and not believing in God.
> >
> > Could you perhaps explain what you mean by "infinity" (whatever that
> > refers to, exactly) being "completed" or "finished". (I assume that
> > completed or finished refer to the same thing.)
> >
> > I don't know of anything in the *subject matter* mathematics where
> > saying that something is "finished" makes sense. Of course a proof may
> > be finished or not, as may some elementary exericises. But a triangle
> > can't be "finished", nor can Klein's four-group. So what would it
> > mean for an infinite set (for example) to be "finished" (or "not
> > finished" for that matter)?
>
> Oh ! How difficult that is ..
>
> _The_ set of _all_ naturals does (actually) exist. Right?
We say some things "exist" or "don't exist" in mathematics: for
example, two groups of order four exist, viz the cyclic 4-group and
the Klein 4-group. No finite skewfield exists (which is a useful thing
to know, because it means you can translate 'tai' in Japanese (or
'corps' in French) as "field" in the context of a finite set).
Formally, in set theory the axiom of infinity is required to ensure
that the set of all integers exists in the formal context. But what of
this is "*actual* existence"??? I've no idea. Can you give examples of
things you think "exist" without "actually existing"? Does Klein's 4-
group "actually exist"? How would one go about testing "actual
existence"?? (In the mathematical sense - none of these thing exist
physically, any more than beauty or jokes.)
Sorry, got tired. Snip rest of the circular evasion.
Brian Chandler
galathaea
instead of "finished"
i like the term "extensional"
in set theory
an infinite set is a container with an infinite amount of
information
one symbol in the container for each element
e.g. for a suitable definition of naturals
N = {0, 1, 2, ...}
but of course
we don't ever deal in infinite information
even so-called infinite structures
can often be specified in a finite amount of information
at least the one's we actually deal with
an axiom system that deals not
in collections of existents obeying a specification
but instead directly with the specification
is "intensional"
for instance
the category theoretic definition of the natural number object
is simply a term that obeys a successor
which distinguishes elements
it is a simple finite diagram
used as a fundament for all iteration in category theory
(i'm not saying category theory is an axiom system
only that it doesn't have extensional representations)
of course
set theorists don't actually write out all of N
they use set builder notation and appropriate formulae
but that's kind of the point
no one ever really deals with infinite information
in one sense
it's a bill clinton distinction
it's all about what "is" is
set theory does not distinguish two specifications
if they have the same elements
intensional systems inherently do distinguish
but allow for proofs of isomorphisms between specs
the key difference conceptually
is that extensional systems are atemporal
everything is an idealised completion
where all applications of a process are collected
as is commonly pointed out
it's platonism
intensional systems actually deal in process and so
either implicitly or explicitly
allow for physical interpretation in temporal models
that
i think
is what most people intuit who say set theory is not physical
and many who challenge cantor's diagonalisation
(or even godel's use)
do so on the extensional forms
it's the whole .9999 =/= 1 belief
that somehow there is information that can be stuffed
into the part of the extension that remains unseen
because set theory uses a toolchest full of abbreviations
to hide away it's extensional nature
of course
cantor's proof is still available in intensional systems
and it's pretty simple and straightforward
the specifications being used are identical
it's just that intensional language uses the specs
and extensional language uses the production
it's my belief that set theory promotes lazy thinking
about issues such as existence and semantics
and i really think this was the major point of the objections
that cantor faced in his day
(particularly kronecker's)
in real life
a function is a process for turning one element into another
in set theory
it is the graph
and so on...
there are intensional versions of all zfc theorems
usually such transformations are minor or involve no extra work
but many people who take the step to intensionalism
realise that the semantics of truth and proof
are just applications of process
and so they become constructivists
this seems to be the path taken by
poincare
kolmogorov
markov
and others of that bent
in fact
i find it interesting that in the field of metamathematics
where they think deeply about such issues
constructivists are quite common
(as they are also in computer science)
in general math
though
where such concerns are considered less
constructivists become less common
just to be clear
constructivists also don't have issue with diagonalisation
(they just understand it better :))
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
MoeBlee
You can ignore me or not, but I'll express what I feel motivated to
express, and sometimes that includes items not just mathematical but
personal too, especially when those personal matters are so clearly a
factor in why the mathematical content is being misrepresented,
misunderstood, or not understood at all.
MoeBlee
mike3
What do you think he should do with it, anyway?
mike3
> On 6 Aug, 21:48, mike3 <mike4...@yahoo.com> wrote:
>
>
>
> > On Aug 6, 2:38 pm, ju...@diegidio.name wrote:
>
> > > On 6 Aug, 21:26, Mariano Suárez-Alvarez
>
> > > <mariano.suarezalva...@gmail.com> wrote:
> > > > On Aug 6, 5:14 pm, ju...@diegidio.name wrote:
> > > > > On 5 Aug, 19:23, mike3 <mike4...@yahoo.com> wrote:
>
> > > > > > Hi.
>
> > > > > > What is it aboutCantor'stheories that makes everyone want to try and
> > > > > > "critique"
> > > > > > them, anyway? And why do they always seem to generate long
> > > > > > discussions?
> > > > > > Why was it that what appears to be the longest thread here (9018 msgs)
> > > > > > started
> > > > > > off with aCantorCritique?
>
> > > > > Because that is where lie the foundations of contemporary mathematics,
> > > > > and on the correctness of those foundations relies the correctness of
> > > > > the whole building.
>
> > > > Actualy, I think that it is a subject that appears
> > > > much more accessible and should-be-common-sense
>
> > > Pardon me, but this is BS. What is at stake _is_ very significant,
> > > despite that some might find the argument trivial. And it even isn't.
> > > Your problem, around here, is that you have lost the sensibility -- or
> > > the energy -- to appreciate the difference(s).
>
> > So are you saying then that it is stupid to feel it "appears"
> > accessible?
>
> It is stupid to be talking about what is irrelevant, only.
>
So then what were you saying was bad about this claim?:
"....that appears much more accessible and should-be-common sense..."
> > I though the "debates" in these threads was about
> > whether or not it was "TRUE". Whole different topic.
>
> Indeed, that's it.
>
Yes, not about whether something is/isn't "accessible", but I'm trying
to figure out what your objection to that statement of it being
accessible
is.
> > I'm confused, could you please help alleviate it?
>
> Logic is power when man is irrational. As Socrates used to say:
> alleviate yourself...
>
So what would happen if man was rational, instead?
David C. Ullrich
<Han.de...@DTO.TUDelft.NL> wrote:
>David C. Ullrich wrote:
>
>> In article <7096$489ada71$82a1e228$29...@news1.tudelft.nl>,
>> Han de Bruijn <Han.de...@DTO.TUDelft.NL> wrote:
>>
>>>David C. Ullrich wrote:
>>>
>>>>Of course the question of whether Cantor's proof of the
>>>>uncountability of the reals is correct is a very important
>>>>question.
>>>>
>>>>But it's also a trivial question. Yes, the proof is correct.
>>>
>>>Preaching like the pope, saying "Of course the question of whether G*d
>>>exists is a very important question. But it's also a trivial question.
>>>Yes, G*d exists."
>>
>> There's a big difference. The pope cannot prove that God exists.
>
>The pope _can_ prove that God exists, _given_ his _own_ assumptions and
>within his _own_ albeit informal overly correct logic.
>
>> I _can_ prove that |P(A)| > |A|. And the proof is very simple.
>
>Sure. But what has _this_ to do with the uncountability of the reals ?
For heaven's sake. Have you ever considered learning some math
before pontificating on it?
>> The fact that I don't write down that proof every time I mention
>> it does not imply that I'm appealing to authority.
>
>I believe you're serious.
>
>Han de Bruijn
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
Tom Potter
"Mensanator" <mensa...@aol.com> wrote in message news:8f7eadfa-6bad-49fc...@z72g2000hsb.googlegroups.com...
> On Aug 6, 12:01=EF=BF=BDam, mike3 <mike4...@yahoo.com> wrote:
> Ah, and I'll bet it is ALSO why they go after Relativity so much
> on sci.physics -- because Einstein was JEWISH!!!!!!!!!!!
- Try doing a Google search on "tom potter".
"Mensanator" raises a good point!
The best measure of a model is its' utility
in a few and open market,
not how it pits one class against another,
one religion against another,
one race against another.
For example, rational, intelligent folks
who want to learn how to judge the value of models
should compare the General Relativity model
to the DNA model.
Note that although General Relativity has been
enormously hyped for one hundred years,
and Einstein was made Time Magazine's
"Man of the Century" and the masses
were conned into thinking that he was the
most intelligent man who ever lived,
that Einstein's model is a Tower of Babel
that wastes time, money and minds
on such pursuits as time travel, warping through space,
the beginning and end of the universe, worm holes,
rubber clocks and rulers, gravitons, etc.
whereas the DNA model is used every day to
improve health, create better crops, create better live stock,
fight crime, reconstruct history, etc.
A mind is a terrible thing to waste.
Thanks "Mensanator" for calling attention to the fact
that anytime anyone questions the value of
General Relativity to society,
that are immediately called "anti-Semitic" and worse.
Your pal,
--
Tom Potter
http://www.geocities.com/tdp1001/index.html
http://notsocrazyideas.blogspot.com
http://www.flickr.com/photos/tom-potter/
http://tdp1001.wiki.zoho.com
http://groups.msn.com/PotterPhotos
http://www.androcles01.pwp.blueyonder.co.uk/dingleberry.htm
** Posted from http://www.teranews.com **
Mike Jr.
> "Mensanator" <mensana...@aol.com> wrote in messagenews:8f7eadfa-6bad-49fc...@z72g2000hsb.googlegroups.com...
Tom,
The Global Positioning System WOULD NOT WORK if corrections derived
from General Relativity where not built into the NAV equations.
http://www.phys.lsu.edu/mog/mog9/node9.html
I worked on GPS and I know this to be true. You are denying plain and
easy to verify fact when you deny General Relativity.
You can spend a few hundred dollars and hold the experimental proof of
General Relativity in your own hands.
http://www.tomtom.com/products/product.php?ID=409
Contrast this to spending $10 billion Euros and waiting two more years
to see the proof of the Higgs boson. General Relativity is a bargain
by comparison.
Which leads to the question that given that the proof of GR is so easy
to obtain, why all this nonsense about Einstein hoax? Why the blatant
denial of easy to verify fact? To the point, what is wrong with you?
--Mike Jr
Mensanator
> "Mensanator" <mensana...@aol.com> wrote in messagenews:8f7eadfa-6bad-49fc...@z72g2000hsb.googlegroups.com...
> > On Aug 6, 12:01=EF=BF=BDam, mike3 <mike4...@yahoo.com> wrote:
You've fucked up the attribution, idiot.
Do they still let you drive?
Or are you too old and senile?
>
> "Mensanator" raises a good point!
>
<snip mind-wasting bullshit>
> Thanks "Mensanator" for calling attention to the fact
> that anytime anyone questions the value of
> General Relativity to society,
> that are immediately called "anti-Semitic" and worse.
What about the Bolsheviks and class warfare?
You're no fun anymore.
>
> Your pal,
>
> --
> Tom Potter
Still doing Google searches for people talking behind your back, eh?
ji...@specsol.spam.sux.com
> Tom,
> The Global Positioning System WOULD NOT WORK if corrections derived
> from General Relativity where not built into the NAV equations.
> http://www.phys.lsu.edu/mog/mog9/node9.html
> I worked on GPS and I know this to be true. You are denying plain and
> easy to verify fact when you deny General Relativity.
It has been explained to him many times by many people with many
references; it doesn't matter he is incapable of comprehending any
of it.
> You can spend a few hundred dollars and hold the experimental proof of
> General Relativity in your own hands.
> http://www.tomtom.com/products/product.php?ID=409
> Contrast this to spending $10 billion Euros and waiting two more years
> to see the proof of the Higgs boson. General Relativity is a bargain
> by comparison.
> Which leads to the question that given that the proof of GR is so easy
> to obtain, why all this nonsense about Einstein hoax? Why the blatant
> denial of easy to verify fact? To the point, what is wrong with you?
Looking at his posts over the years, my guess is senility which is
getting worse.
--
Jim Pennino
Remove .spam.sux to reply.
Ian Parker
> "Mensanator" <mensana...@aol.com> wrote in messagenews:8f7eadfa-6bad-49fc...@z72g2000hsb.googlegroups.com...
> > On Aug 6, 12:01=EF=BF=BDam, mike3 <mike4...@yahoo.com> wrote:
> > Ah, and I'll bet it is ALSO why they go after Relativity so much
> > on sci.physics -- because Einstein was JEWISH!!!!!!!!!!!
>
> - Try doing a Google search on "tom potter".
>
> "Mensanator" raises a good point!
>
> The best measure of a model is its' utility
> in a few and open market,
> not how it pits one class against another,
> one religion against another,
> one race against another.
>
> For example, rational, intelligent folks
> who want to learn how to judge the value of models
> should compare the General Relativity model
> to the DNA model.
>
Each strain of Antrax has its own signiture.
http://news.bbc.co.uk/1/hi/world/americas/7547823.stm
The strain Dr. Ivins was working on had its own unique signiture. The
FBI rapidly established that Antrax came from Fort Detrick because of
the DNA signiture. Why it did not nail Ivins at that point I really
don't know. The only possible explanation is a cover up.
The head of the FBI Robert Mueller idiot that he was got up on his
hind legs and said that it was a second wave for Al Qaeda. DNA proved
that to be rubbish.
http://en.wikipedia.org/wiki/2001_anthrax_attacks
Mrs. Stevens thinks that Ivins was unstable. Personally I don't buy
that, there is clear evidence of a conspiracy viz the fact that Ivins
could have been nailed in 2002.
As far as Relativity is concerned I find it difficult to rate science
in order of importance. In a sense every bit is equally important. If
Relativity had been generally believed in 1945 we would have been
spared antigravity and people like you justifying the unjustifiable.
- Ian Parker
Androcles
"Mike Jr." <n00...@comcast.net> wrote in message
news:0f038bd4-eae7-4d3b...@y38g2000hsy.googlegroups.com...
| Tom,
| The Global Positioning System WOULD NOT WORK if corrections derived
| from General Relativity where not built into the NAV equations.
Idiotic nonsense.
http://www.androcles01.pwp.blueyonder.co.uk/GPS/GPS.htm
Angus Rodgers
<tdp...@yahoo.com> wrote:
>Thanks "Mensanator" for calling attention to the fact
>that anytime anyone questions the value of
>General Relativity to society,
>that are immediately called "anti-Semitic" and worse.
Do you have any evidence of Herbert Dingle ever having even
been accused - let alone found guilty - of anti-Semitism?
--
Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
Mike
> "Mike Jr." <n00s...@comcast.net> wrote in message
I was down at Schriever recently. Your reference is apply titled;
Idiotic nonsense indeed.
I am sure that no amount of math will inform your thinking. But other
readers can refer to
http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&key=SP96
--Mike Jr
--Mike JR
Androcles
"Mike" <n00...@comcast.net> wrote in message
news:ec944901-7dd1-411d...@t54g2000hsg.googlegroups.com...
You don't know any math, you fuckin' idiot, you fucking idiot.
GPS calculations are all done in the receiver, the receiver, you moron, you
moron.
You don't even know the difference between "aptly", "apply" and "apples",
cretin, cretin.
--Androcles --Androcles
Ian Parker
> On Sat, 9 Aug 2008 22:56:25 +0800, "Tom Potter"
>
> >Thanks "Mensanator" for calling attention to the fact
> >that anytime anyone questions the value of
> >General Relativity to society,
> >that are immediately called "anti-Semitic" and worse.
>
> Do you have any evidence of Herbert Dingle ever having even
> been accused - let alone found guilty - of anti-Semitism?
>
> --
> Angus Rodgers
> (twirlip@ eats spam; reply to angusrod@)
> Contains mild peril
You look at some of his postings. Do a search on Tom Potter, Jews
- Ian Parker
Angus Rodgers
<ianpa...@gmail.com> wrote:
>On 9 Aug, 18:24, Angus Rodgers <twir...@bigfoot.com> wrote:
>> On Sat, 9 Aug 2008 22:56:25 +0800, "Tom Potter"
>>
>> <tdp1...@yahoo.com> wrote:
>> >Thanks "Mensanator" for calling attention to the fact
>> >that anytime anyone questions the value of
>> >General Relativity to society,
>> >that are immediately called "anti-Semitic" and worse.
>>
>> Do you have any evidence of Herbert Dingle ever having even
>> been accused - let alone found guilty - of anti-Semitism?
>
>You look at some of his postings. Do a search on Tom Potter, Jews
I know about Tom Potter. I was arguing against him!
What visual resemblance is there between the strings
"Herbert Dingle" and "Tom Potter"?